Let the sum of the maximum and the minimum values of the function be

MATHEMATICS · Single correct · AoPS · Mathematics · More Inequalities · More Inequalities

Problem

Let the sum of the maximum and the minimum values of the function

f(x) = \frac{2x^2 - 3x + 8}{2x^2 + 3x + 8}

\frac{m}{n}

, where

\text{gcd}(m, n) = 1

. Then

m + n

is equal to: (A) 182 (B) 217 (C) 195 (D) 201